Measurement equipment is important to the manufacture, sale, operation, and maintenance of modern electronic and optical devices and systems. A variety of measurement equipment is available such as vector analyzers, spectrum analyzers, power meters, etc. For purposes of illustration only, some of the following description is offered in the context of an optical vector analyzers (OVA), but the present invention is not limited to OVAs but applies to any suitable measurement device. One example OVA is described in commonly-assigned U.S. patent application Ser. No. 10/005,819, entitled “APPARATUS AND METHOD FOR THE COMPLETE CHARACTERIZATION OF OPTICAL DEVICES INCLUDING LOSS, BIREFRINGENCE AND DISPERSION EFFECTS,” filed on Dec. 14, 2001, the disclosure of which is incorporated by reference. Most such measurement equipment allows for some sort of calibration in an attempt to remove the affect of measurement equipment errors from the measurement of a device under test (DUT). Typically, calibration involves testing a device having known characteristics which are compared to the measured characteristics in order to determine appropriate corrections or compensations to the measurement equipment output.
Consider fiber optic components as example DUTs. A fiber optic component can be accurately modeled using linear systems theory where a 2×2 complex matrix is used to represent a transfer function that characterizes the affect the fiber optic component has on light. If light passes through a series of components, the total transfer function is given by the product of these matrices.Ēout= CBAĒin= XEin  (1)This is illustrated in FIG. 1 which shows light Ē propagating through a series of optical components, each labeled with its corresponding matrix A, B, and C. The entire set of optical components can be represented as a single component matrix X that encompasses all of the properties of the individual components, as shown in FIG. 2.
Measurement equipment (like an OVAs) typically determines a matrix corresponding to the transfer function for an individual optical DUT. See for example the illustration in FIG. 3. Such a matrix may be, for example, a Jones matrix. The connections from the measurement equipment 10 to the DUT 12 and optical components within or otherwise associated the measurement equipment (hereafter “internal optics”) affect the light, and thus, the accuracy of the measurement matrix. These connections and internal optics occur at both the input and the output of the measurement equipment. A “real” measurement equipment can be represented using an ideal (perfect) measurement equipment with source and detector error matrices, D (14) and S (16), as shown in FIG. 4.
If the source and detector error matrices, D and S, can be determined, they can be inverted and used to operate on the measured DUT matrix, M, to find a corrected matrix Mc:Mc=D−1MS−1=D−1DXSS−1=X  (2)Mc is an accurate measurement of the device, free of the errors created by imperfect measurement equipment and connectors. The source and detector error matrices can be determined if the Device Under Test (DUT) is replaced with a device R known to be free of loss and significant dispersion, e.g., a short section of optical fiber. Although a short fiber is essentially lossless, mild bends in the fiber can cause the fiber section to change the polarization state of the light. The lossless transfer function matrix that corresponds to the fiber section is commonly known as a “rotation” matrix R, which is illustrated in FIG. 5.
Because the rotation matrix R is lossless, there can not be any change in loss for different input polarization states to the fiber section. In other words, the fiber section has zero Polarization Dependent Loss (PDL). If the fiber section is connected to the imperfect measurement equipment, and the inverted source and detector error correction matrices (D−1 and S−1) are applied to the output produced by the measurement equipment, then the output should be lossless. If the inverted source and detector error correction matrices (D−1 and S−1) are correct, a lossless matrix will result for all rotational matrices R. In other words, if the fiber connecting the source to the detector is re-oriented, there will still be zero PDL and zero insertion loss produced by the fiber section.
The product of two rotational matrices is always a rotational matrix. Further, multiplication of any matrix by a rotation matrix will not change its PDL or insertion loss characteristics. This is similar to a situation where adding a length of fiber (or cutting off a length of fiber) from a component lead does not change the component's PDL or insertion loss. Therefore, if the inverted source and detector error matrices are multiplied by rotational matrices, the measured PDL or insertion loss of the device being measured will not change.
The transfer matrix of the lossless fiber section at three different orientations or polarizations produces three measured matrices: M0= DR0 S,  (3) M1= DR1 S,and  (4) M2= DR2 S.  (5)From these three measured matrices, the following detector and source correction matrices can be determined: D′= RD D−1,and  (6) S′= S−1 Rs.  (7)The process by which these detector and source correction matrices D′ and S′ are determined from the three measurements M0, M1, and M2, which were made by an imperfect measurement system of three lossless rotation matrices, is referred to as the “Basic Calibration Algorithm (BCA),” and is set forth below:BCAS( M0, M1, M2)= S′= S−1 Rs  (8)BCAD( M0, M1, M2)= D′= RD D−1  (9)where BCAs is the basic calibration algorithm for calculating the source error correction matrix S′, and BCAD is the basic calibration algorithm for calculating the detector error correction matrix D′.
That process is as follows. Define a new intermediate matrix, Y, as the inverse of M0, Y= M0−1. Calculate the eigenvectors of the product of Y and M1 and assemble these into an eigen-matrix, Ē, that can be used to diagonalize M1 Y. The relative amplitudes of the eigenvectors are chosen such that
                    E        _                                              ⁢                  -          1                      ⁢                  M        _            1        ⁢          YE      _        =            [                                                  ⅇ                              -                                  φ                  1                                                                          0                                                0                                              ⅇ                              -                                  φ                  2                                                                        ]        .  This matrix is “diagonal” because the off-diagonal entries are zero. The matrix is also lossless because the magnitude of the entries on the diagonal is unity. Therefore, the matrix also has zero PDL and satisfies the criteria of correcting for PDL effects in the detector matrix, D. A detailed description of the calculation of eigenvectors and their application to diagonalizing matrices can be found in “Elementary Linear Algebra,” by Howard Anton (John Wiley and Sons, New York).
There is a family of matrices that will diagonalize M1 and produce unity amplitude entries. In other words, the eigenmatrix, Ē, is only one solution. Therefore, although Ē will properly diagonalize M1 Y, and M0 Y, Ē is not fully determined. We can create another matrix, W, which has the property that it diagonalizes both M1 Y and M0 Y, and yet has an additional degree of freedom. This matrix, W, is created by multiplying the eigenmatrix, Ē, by a matrix having PDL, but no off-diagonal terms:
                                          W            _                    =                                    E              _                        ⁡                          [                                                                    r                                                        0                                                                                        0                                                                              1                      r                                                                                  ]                                      ,        where        ,                            (        10        )                                                                    W              _                                                                                  ⁢                              -                1                                              =                                    [                                                                                          1                      r                                                                            0                                                                                        0                                                        r                                                              ]                        ⁢                                          E                _                                            -                1                                                    ,                            (        11        )                                                                                    W                _                                                                                              ⁢                                  -                  1                                                      ⁢                                          M                _                            1                        ⁢                          YW              _                                =                      [                                                                                ⅇ                                          -                                              φ                        1                                                                                                              0                                                                              0                                                                      ⅇ                                          -                                              φ                        2                                                                                                                  ]                          ,                                  ⁢        and                            (        12        )                                                                                    W                _                            ⁢                                                                                  -              1                                ⁢                                    M              _                        0                    ⁢                      YW            _                          =                              [                                                            1                                                  0                                                                              0                                                  1                                                      ]                    .                                    (        13        )            If we apply this correction to the matrix formed by the product of M2 and Y, i.e., M2 Y, in order to correct for the errors induced by the detector matrix, we get:
                                                        W              _                                                                                  ⁢                              -                1                                              ⁢                                    M              _                        1                    ⁢                      YW            _                          =                              [                                                                                1                    r                                                                    0                                                                              0                                                  r                                                      ]                    ⁢                                    E              _                                                                                  ⁢                              -                1                                              ⁢                                    M              _                        2                    ⁢                                    YE              _                        ⁡                          [                                                                    r                                                        0                                                                                        0                                                                              1                      r                                                                                  ]                                                          (        14        )            A search algorithm can be used to determine the value of the real-positive number, r, such that the polarization dependent loss of the entire matrix, W−1 M1 YW, is zero.
We now have two matrices that can be used to correct for the errors induced by the source and detector matrices. Given an arbitrary measurement, X, containing the effects of the source and detector matrix, these errors can be removed by applying the matrices as below: Xcorrected= W−1 XYW= D′ XS′  (15)where we now see that, D′= W−1= DRD,  (16)and S′= YW= SRS.  (17)The two unknown rotation matrices RD and RS are equivalent to a fiber section connected to the measurement equipment, and as a result, have no affect on the DUT measurement. So equations (6) and (7) permit calculation of the inverted detector and source error matrices that allow determination of the DUT corrected matrix Mc, as defined in equation (2). This is illustrated in FIG. 6.
When conducting tests of optical DUTs, such as wavelength filters and dispersion compensators, it is advantageous to be able to remove the source and detector errors from the DUT measurement using properly determined source and detector error matrices. The source and detector error matrices may be determined by connecting the lossless calibration device between the source and detector connectors, measuring the three different rotation matrices, and then calculating the source and detector error matrices, as described above.
FIG. 7 shows a fiber-loop polarization controller 20 connected between the source and detector. The fiber-loop polarization controller is adjusted to three different polarizations, e.g., by moving “paddles” of the fiber-loop polarization controller to three distinct positions to obtain the three distinct measurement matrices M0-M2. The three measurement matrices M0-M2 may be determined using a quarter-wave fiber loop positioned at each of 0°, 45°, and 90°. From M0-M2, the source and detector error correction matrices may be calculated.
A significant drawback with this calibration method is that the device under test must be disconnected from the measurement equipment in order to re-calibrate the measurement equipment. Such re-calibration is often necessary because characteristics of optical components internal to the measurement equipment often “drift.” This drift is primarily caused by thermal changes, and a change of 0.5° Celsius can cause the measurement equipment to drift out of calibration. As a result, re-calibration of the internal components must be carried out frequently. This frequent re-calibration is problematic because the device under test must be disconnected every re-calibration.
The present invention overcomes this significant problem by providing another calibration path referred to as a “re-calibration path.” The re-calibration path may include a fiber-loop polarization controller. In one non-limiting example, the re-calibration path could be internal to the test equipment, but it may also be external. The re-calibration path is distinct from the “main calibration path,” and advantageously, the re-calibration may occur after the initial, main calibration and without having to disconnect the device under test.
Another inventive feature relates to the measurement equipment source and detector connectors for connecting the device under test to the test equipment. Those connectors may not be included in the re-calibration calculations. But because these connectors can influence the calibration, e.g., they can add as much as a 0.07 dB error to both PDL and insertion loss, the connectors should be accounted for in some way in the re-calibration. Fortunately, the source and detector connector characteristics do not drift much with time or with temperature, so they need not be re-calibrated often. Thus, once the source and detector connector calibrations are initially determined during the main calibration, they can be re-used with the re-calibration results to provide new correction matrices.
With the main initial calibration and one or more re-calibrations, the DUT may remain connected and accurately measured for long periods of time. This is a significant advance for measurement equipment.
Certain aspects of the invention will now be described in accordance with certain features recited in certain claims. One aspect relates to a method for calibrating apparatus for measuring one or more characteristics of an optical element. A calibration operation is performed using a first calibration path without the optical element having to be operatively-decoupled from the apparatus. The optical element to be tested may be coupled for testing between the source connector and a detector connector of the apparatus. A second calibration operation may also be performed, (typically before device testing), using a second calibration path. But when performing the second calibration, the optical element is operatively decoupled from the apparatus.
The first calibration path may include a fiber-loop polarization controller that remains in the first calibration path even when the optical element under test is coupled to the apparatus. That polarization controller operates as a rotation matrix during the first calibration operation. The first polarization controller is moved to multiple positions, and one or more first calibration corrections is determined for the apparatus at each of the multiple positions. The first calibration corrections are then used to update the calibration initially performed.
More specifically, the calibration includes determining a source correction matrix that corrects for an affect of one or more optical components coupled between a light source in the apparatus and a source connector. A detector correction matrix is also determined that corrects for an effect of one or more optical components coupled between a light detector in the apparatus and a detector connector. During testing, a DUT is operatively-coupled to these connectors. The first calibration operation includes determining an optical transfer function through the fiber loop polarization controller at multiple positions. The source and detector correction matrices are then determined using the optical transfer functions determined at each of the multiple positions.
In a non-limiting example embodiment, the first calibration corrections do not account for the source and detector connectors. Accordingly, the re-calibration uses the source and detector error correction matrices from the first calibration operations and combines them with the corrections for the source connector and error detector initially determined during the second calibration operation. A controller switches optical switches to select either the first calibration path or the second calibration path. Single port and multi-port/multi-channel implementations are described.